Initial Data Wrangling
## # A tibble: 22,052 x 8
## SPECIES_NAME FISH_ID SCIENTIFIC_FAMILY YEAR DIET LOCATION MARINE_RESERVE
## <chr> <dbl> <chr> <dbl> <chr> <chr> <chr>
## 1 Blue Angelfish 1 Other 1998 Spong… CH Yes
## 2 Blue Angelfish 1 Other 1998 Spong… DG Yes
## 3 Blue Angelfish 1 Other 1998 Spong… SB No
## 4 Blue Angelfish 1 Other 1998 Spong… SC No
## 5 Blue Angelfish 1 Other 1998 Spong… TF No
## 6 Blue Angelfish 1 Other 2000 Spong… CP Yes
## 7 Blue Angelfish 1 Other 2000 Spong… DG Yes
## 8 Blue Angelfish 1 Other 2000 Spong… SC No
## 9 Blue Angelfish 1 Other 2000 Spong… CH Yes
## 10 Blue Angelfish 1 Other 2000 Spong… SB No
## # … with 22,042 more rows, and 1 more variable: DENSITY_INDEX <dbl>
Unique Datasets
Math
## [1] 16844
## [1] 1348
## [1] 1533
## [1] 411
Response Patterning

Mathematical Summaries
Overall Summary Statistics for Eleven Dive Sites on Grand Cayman Island
|
Location
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
BB
|
0.4114386
|
0.8404847
|
0.0202777
|
1718
|
|
CH
|
0.3790222
|
0.8283496
|
0.0264742
|
979
|
|
CP
|
0.4427012
|
0.8590365
|
0.0173410
|
2454
|
|
CR
|
0.4992615
|
0.8826122
|
0.0212879
|
1719
|
|
DG
|
0.4622359
|
0.8855441
|
0.0170391
|
2701
|
|
ER
|
0.5200795
|
0.9229405
|
0.0340896
|
733
|
|
SB
|
0.4458110
|
0.8681177
|
0.0176143
|
2429
|
|
SC
|
0.3418897
|
0.7728271
|
0.0148786
|
2698
|
|
SH
|
0.4241696
|
0.8505619
|
0.0205328
|
1716
|
|
SV
|
0.4829153
|
0.8878970
|
0.0179273
|
2453
|
|
TF
|
0.4861403
|
0.8937834
|
0.0180498
|
2452
|
Overall Summary Statistics for Marine Reserve VS Non-Reserve Sites on
Grand Cayman Island
|
Reserve Type
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
No
|
0.4199377
|
0.8451827
|
0.0087656
|
9297
|
|
Yes
|
0.4592603
|
0.8743441
|
0.0077418
|
12755
|
Overall Summary Statistics for Species Primary Diets on Grand Cayman
Island
|
Diet
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
Algae
|
0.8157071
|
1.0791521
|
0.0211761
|
2597
|
|
Coral
|
1.1197525
|
1.0038735
|
0.0474286
|
448
|
|
Crustaceans
|
0.4475921
|
0.8598790
|
0.0108516
|
6279
|
|
Echinoids
|
0.3550889
|
0.7826984
|
0.0412518
|
360
|
|
Fish
|
0.3999007
|
0.7719094
|
0.0117715
|
4300
|
|
Sponges
|
0.4879182
|
0.7743653
|
0.0204134
|
1439
|
|
Unidentified
|
0.1628468
|
0.5479348
|
0.0074654
|
5387
|
|
Zooplankton
|
0.7284863
|
1.2434362
|
0.0352828
|
1242
|
Overall Summary Statistics Across Scientific Families on Grand Cayman
Island
|
Family
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
Apogonidae
|
0.2023553
|
0.6248673
|
0.0268900
|
540
|
|
Carangidae
|
0.1822212
|
0.5963663
|
0.0181553
|
1079
|
|
Gobiidae
|
0.1782912
|
0.6100019
|
0.0151744
|
1616
|
|
Haemulidae
|
0.3256079
|
0.7707249
|
0.0203316
|
1437
|
|
Holocentridae
|
1.1331251
|
1.1666672
|
0.0505340
|
533
|
|
Labridae
|
0.4719138
|
0.8630698
|
0.0235422
|
1344
|
|
Lutjanidae
|
0.5678172
|
0.9033246
|
0.0301780
|
896
|
|
Other
|
0.4173957
|
0.8162026
|
0.0086644
|
8874
|
|
Pomacentridae
|
1.1796572
|
1.2673786
|
0.0360057
|
1239
|
|
Scaridae
|
0.7079198
|
1.0171146
|
0.0297866
|
1166
|
|
Serranidae
|
0.2995883
|
0.6482272
|
0.0124798
|
2698
|
|
Sparidae
|
0.2442227
|
0.7033578
|
0.0280224
|
630
|
Overall Summary Statistics of Density Index on Grand Cayman Island
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
0.4426821
|
0.8623694
|
0.0058072
|
22052
|
Non-Zero Summary Statistics for Eleven Dive Sites on Grand Cayman Island
|
Location
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
BB
|
1.910410
|
0.6446859
|
0.0335156
|
370
|
|
CH
|
1.922605
|
0.7155327
|
0.0515052
|
193
|
|
CP
|
1.844463
|
0.6990244
|
0.0288028
|
589
|
|
CR
|
1.803005
|
0.6796540
|
0.0311519
|
476
|
|
DG
|
1.903200
|
0.6970671
|
0.0272159
|
656
|
|
ER
|
1.906091
|
0.6915084
|
0.0488970
|
200
|
|
SB
|
1.893138
|
0.6780724
|
0.0283516
|
572
|
|
SC
|
1.844837
|
0.6706988
|
0.0299946
|
500
|
|
SH
|
1.885686
|
0.6778973
|
0.0345041
|
386
|
|
SV
|
1.871392
|
0.6753849
|
0.0268441
|
633
|
|
TF
|
1.883122
|
0.6806016
|
0.0270515
|
633
|
Non-Zero Summary Statistics for Marine Reserve VS Non-Reserve Sites on
Grand Cayman Island
|
Reserve Type
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
No
|
1.881523
|
0.6711375
|
0.0147334
|
2075
|
|
Yes
|
1.869730
|
0.6892262
|
0.0123135
|
3133
|
Non-Zero Summary Statistics for Species Primary Diets on Grand Cayman
Island
|
Diet
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
Algae
|
2.058689
|
0.6160146
|
0.0192036
|
1029
|
|
Coral
|
1.878836
|
0.5118014
|
0.0313217
|
267
|
|
Crustaceans
|
1.869881
|
0.6551331
|
0.0168986
|
1503
|
|
Echinoids
|
1.800451
|
0.7087813
|
0.0841169
|
71
|
|
Fish
|
1.640814
|
0.6391348
|
0.0197429
|
1048
|
|
Sponges
|
1.543108
|
0.5171518
|
0.0242445
|
455
|
|
Unidentified
|
1.758027
|
0.6611286
|
0.0295962
|
499
|
|
Zooplankton
|
2.692798
|
0.6498730
|
0.0354535
|
336
|
Non-Zero Summary Statistics Across Scientific Families on Grand Cayman
Island
|
Family
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
Apogonidae
|
1.986762
|
0.5352753
|
0.0721765
|
55
|
|
Carangidae
|
1.908900
|
0.6560420
|
0.0646417
|
103
|
|
Gobiidae
|
2.072795
|
0.6319028
|
0.0535973
|
139
|
|
Haemulidae
|
1.925508
|
0.6568684
|
0.0421381
|
243
|
|
Holocentridae
|
2.220425
|
0.4988204
|
0.0302454
|
272
|
|
Labridae
|
1.781607
|
0.6914175
|
0.0366451
|
356
|
|
Lutjanidae
|
1.823528
|
0.5735640
|
0.0343384
|
279
|
|
Other
|
1.747980
|
0.6811335
|
0.0147968
|
2119
|
|
Pomacentridae
|
2.361220
|
0.6505770
|
0.0261489
|
619
|
|
Scaridae
|
1.984217
|
0.6046368
|
0.0296448
|
416
|
|
Serranidae
|
1.519341
|
0.5268009
|
0.0228397
|
532
|
|
Sparidae
|
2.051471
|
0.6689056
|
0.0772386
|
75
|
Non-Zero Summary Statistics of Density Index on Grand Cayman Island
|
Mean Density Index
|
Standard Deviation
|
Standard Error
|
Sample Size
|
|
1.874429
|
0.6820364
|
0.0094509
|
5208
|
Hypothesis Testing
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 10 7.1728 2.151e-11 ***
## 22041
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 11.186 0.0008255 ***
## 22050
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 211.16 < 2.2e-16 ***
## 22044
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 185.32 < 2.2e-16 ***
## 22040
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 10 0.7767 0.6516
## 5197
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 3.4425 0.0636 .
## 5206
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 9.5329 8.094e-12 ***
## 5200
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 15.452 < 2.2e-16 ***
## 5196
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## NoZero_Levene_Test NoZero_Levene_PVals NoZero_Levene_Interpret
## 1 Diet 8.094e-12 Unequal Variance
## 2 Family 2.2e-16 Unequal Variance
## 3 Location 0.6516 Equal Variance
## 4 Reserve 0.0636 Equal Variance
Summary of Levene Test Results
|
Test Variable
|
Resulting P-Value
|
Interpretation
|
|
Diet
|
2.2e-16
|
Unequal Variance
|
|
Family
|
2.2e-16
|
Unequal Variance
|
|
Location
|
2.151e-11
|
Unequal Variance
|
|
Reserve
|
0.0008255
|
Unequal Variance
|
Non-Zero Data Summary of Levene Test Results
|
Test Variable
|
Resulting P-Value
|
Interpretation
|
|
Diet
|
8.094e-12
|
Unequal Variance
|
|
Family
|
2.2e-16
|
Unequal Variance
|
|
Location
|
0.6516
|
Equal Variance
|
|
Reserve
|
0.0636
|
Equal Variance
|
##
## One-way analysis of means (not assuming equal variances)
##
## data: DENSITY_INDEX and LOCATION
## F = 7.8556, num df = 10.0, denom df = 7185.7, p-value = 1.144e-12
##
## Welch Two Sample t-test
##
## data: DENSITY_INDEX by MARINE_RESERVE
## t = -3.3624, df = 20405, p-value = 0.0007742
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.06224556 -0.01639972
## sample estimates:
## mean in group No mean in group Yes
## 0.4199377 0.4592603
##
## One-way analysis of means (not assuming equal variances)
##
## data: DENSITY_INDEX and DIET
## F = 233.2, num df = 7.0, denom df = 3027.4, p-value < 2.2e-16
##
## One-way analysis of means (not assuming equal variances)
##
## data: DENSITY_INDEX and SCIENTIFIC_FAMILY
## F = 119.48, num df = 11.0, denom df = 4526.4, p-value < 2.2e-16
## Df Sum Sq Mean Sq F value Pr(>F)
## LOCATION 10 5.4 0.5368 1.154 0.317
## Residuals 5197 2416.8 0.4650
##
## Two Sample t-test
##
## data: DENSITY_INDEX by MARINE_RESERVE
## t = 0.61085, df = 5206, p-value = 0.5413
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.02605401 0.04963955
## sample estimates:
## mean in group No mean in group Yes
## 1.881523 1.869731
##
## One-way analysis of means (not assuming equal variances)
##
## data: DENSITY_INDEX and DIET
## F = 137.34, num df = 7.00, denom df = 845.43, p-value < 2.2e-16
##
## One-way analysis of means (not assuming equal variances)
##
## data: DENSITY_INDEX and SCIENTIFIC_FAMILY
## F = 75.462, num df = 11.00, denom df = 734.19, p-value < 2.2e-16
## NoZero_TANOVA_Test NoZero_Test_Type NoZero_TANOVA_PVals
## 1 Diet Welch ANOVA 2.2e-16
## 2 Family Welch ANOVA 2.2e-16
## 3 Location Standard ANOVA 0.317
## 4 Reserve Equal Variance T-Test 0.5413
## NoZero_Result_Interpret
## 1 True Mean Difference Not 0
## 2 True Mean Difference Not 0
## 3 True Mean Difference = 0
## 4 True Mean Difference = 0
Summary of ANOVA and T-Test Results
|
Test Variable
|
Test Type
|
Resulting P-Value
|
Interpretation
|
|
Diet
|
Welch ANOVA
|
2.2e-16
|
True Mean Difference Not 0
|
|
Family
|
Welch ANOVA
|
2.2e-16
|
True Mean Difference Not 0
|
|
Location
|
Welch ANOVA
|
1.144e-12
|
True Mean Difference Not 0
|
|
Reserve
|
Welch T-Test
|
0.0007742
|
True Mean Difference Not 0
|
Non-Zero Data Summary of ANOVA and T-Test Results
|
Test Variable
|
Test Type
|
Resulting P-Value
|
Interpretation
|
|
Diet
|
Welch ANOVA
|
2.2e-16
|
True Mean Difference Not 0
|
|
Family
|
Welch ANOVA
|
2.2e-16
|
True Mean Difference Not 0
|
|
Location
|
Standard ANOVA
|
0.317
|
True Mean Difference = 0
|
|
Reserve
|
Equal Variance T-Test
|
0.5413
|
True Mean Difference = 0
|
Slope Investigation Plots


MODELING WITH TWO PARTS
LOGISTIC REGRESSION PORTION
## SCIENTIFIC_FAMILY YEAR DIET LOCATION
## Length:22052 Min. :1998 Length:22052 Length:22052
## Class :character 1st Qu.:2004 Class :character Class :character
## Mode :character Median :2010 Mode :character Mode :character
## Mean :2009
## 3rd Qu.:2014
## Max. :2018
## MARINE_RESERVE DENSITY_INDEX
## Length:22052 Min. :0.0000
## Class :character 1st Qu.:0.0000
## Mode :character Median :0.0000
## Mean :0.2362
## 3rd Qu.:0.0000
## Max. :1.0000
## [1] 16844
##
## Call:
## glm(formula = DENSITY_INDEX ~ ., family = binomial(link = "logit"),
## data = CAYMAN_LOGISTIC_DATA)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6089 -0.7642 -0.5179 -0.3165 2.5987
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -98.832908 5.832728 -16.945 < 2e-16 ***
## SCIENTIFIC_FAMILYCarangidae -0.979265 0.195182 -5.017 5.24e-07 ***
## SCIENTIFIC_FAMILYGobiidae 0.318873 0.182661 1.746 0.080862 .
## SCIENTIFIC_FAMILYHaemulidae 0.058979 0.173020 0.341 0.733192
## SCIENTIFIC_FAMILYHolocentridae 1.707774 0.184549 9.254 < 2e-16 ***
## SCIENTIFIC_FAMILYLabridae 0.787200 0.172325 4.568 4.92e-06 ***
## SCIENTIFIC_FAMILYLutjanidae 0.602563 0.179902 3.349 0.000810 ***
## SCIENTIFIC_FAMILYOther 0.465475 0.157401 2.957 0.003104 **
## SCIENTIFIC_FAMILYPomacentridae 1.497226 0.160466 9.331 < 2e-16 ***
## SCIENTIFIC_FAMILYScaridae 0.622229 0.174523 3.565 0.000363 ***
## SCIENTIFIC_FAMILYSerranidae 0.210358 0.167105 1.259 0.208090
## SCIENTIFIC_FAMILYSparidae -0.379678 0.204038 -1.861 0.062770 .
## YEAR 0.048537 0.002902 16.726 < 2e-16 ***
## DIETCoral 1.160950 0.118867 9.767 < 2e-16 ***
## DIETCrustaceans -0.434950 0.081939 -5.308 1.11e-07 ***
## DIETEchinoids -0.674088 0.149795 -4.500 6.79e-06 ***
## DIETFish -0.085372 0.086043 -0.992 0.321101
## DIETSponges -0.100493 0.086653 -1.160 0.246164
## DIETUnidentified -1.497794 0.088101 -17.001 < 2e-16 ***
## DIETZooplankton -0.630666 0.091735 -6.875 6.21e-12 ***
## LOCATIONCH -0.079906 0.105462 -0.758 0.448646
## LOCATIONCP 0.124029 0.079893 1.552 0.120558
## LOCATIONCR 0.204391 0.085011 2.404 0.016204 *
## LOCATIONDG 0.188154 0.078357 2.401 0.016339 *
## LOCATIONER 0.026480 0.109212 0.242 0.808418
## LOCATIONSB 0.143546 0.080298 1.788 0.073827 .
## LOCATIONSC -0.197840 0.081186 -2.437 0.014815 *
## LOCATIONSH -0.105803 0.087627 -1.207 0.227269
## LOCATIONSV 0.233321 0.079222 2.945 0.003228 **
## LOCATIONTF 0.259324 0.079259 3.272 0.001068 **
## MARINE_RESERVEYes NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 24108 on 22051 degrees of freedom
## Residual deviance: 21575 on 22022 degrees of freedom
## AIC: 21635
##
## Number of Fisher Scoring iterations: 5
##
## Call:
## glm(formula = DENSITY_INDEX ~ SCIENTIFIC_FAMILY, family = binomial(link = "logit"),
## data = CAYMAN_LOGISTIC_DATA)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1950 -0.7387 -0.6628 -0.4241 2.2151
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.17682 0.14227 -15.301 < 2e-16 ***
## SCIENTIFIC_FAMILYCarangidae -0.07192 0.17599 -0.409 0.682793
## SCIENTIFIC_FAMILYGobiidae -0.18648 0.16765 -1.112 0.266011
## SCIENTIFIC_FAMILYHaemulidae 0.58481 0.15873 3.684 0.000229 ***
## SCIENTIFIC_FAMILYHolocentridae 2.21810 0.16658 13.316 < 2e-16 ***
## SCIENTIFIC_FAMILYLabridae 1.15606 0.15512 7.453 9.14e-14 ***
## SCIENTIFIC_FAMILYLutjanidae 1.38316 0.15952 8.671 < 2e-16 ***
## SCIENTIFIC_FAMILYOther 1.01748 0.14443 7.045 1.86e-12 ***
## SCIENTIFIC_FAMILYPomacentridae 2.17520 0.15320 14.199 < 2e-16 ***
## SCIENTIFIC_FAMILYScaridae 1.58743 0.15485 10.251 < 2e-16 ***
## SCIENTIFIC_FAMILYSerranidae 0.77282 0.15027 5.143 2.71e-07 ***
## SCIENTIFIC_FAMILYSparidae 0.17534 0.18808 0.932 0.351224
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 24108 on 22051 degrees of freedom
## Residual deviance: 22825 on 22040 degrees of freedom
## AIC: 22849
##
## Number of Fisher Scoring iterations: 4
## [1] 0.1015609
## [1] 0.168655
## [1] 0.5095238
## [1] 0.2642606
## [1] 0.3107019
## [1] 0.2382097
## [1] 0.4988
## [1] 0.3560454
## [1] 0.1966792
LINEAR MIXED EFFECT
How has density index values changed over time on Grand Cayman
Island? How do density index values vary across dive sites?
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8436.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6607 -0.6235 -0.0347 0.6186 3.8503
##
## Random effects:
## Groups Name Variance Std.Dev.
## SPECIES_NAME (Intercept) 0.1947 0.4413
## Residual 0.2653 0.5151
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.73686 0.03138 227.75030 55.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 0.4231606
Unconditional Growth Model
\[
Y_{ij}=\alpha_{0} +
\beta_{0}\textrm{Year2013}_{ij}+u_{i}+v_{i}\textrm{Year2013}_{ij} +
\epsilon_{ij}
\]
where \(\epsilon_{ij}\sim
N(0,\sigma^2)\) and
\[
\left[ \begin{array}{c}
u_{i} \\ v_{i}
\end{array} \right] \sim N \left( \left[
\begin{array}{c}
0 \\ 0
\end{array} \right], \left[
\begin{array}{cc}
\sigma_{u}^{2} & \\
\rho_{uv}\sigma_{u}\sigma_{u} & \sigma_{v}^{2}
\end{array} \right] \right) .
\]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + (YEAR1998 | SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8357.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3173 -0.6166 -0.0355 0.6184 4.0456
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## SPECIES_NAME (Intercept) 0.280071 0.52922
## YEAR1998 0.001437 0.03791 -0.58
## Residual 0.253967 0.50395
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.854212 0.044437 166.901884 41.727 < 2e-16 ***
## YEAR1998 -0.015891 0.004004 114.793187 -3.969 0.000126 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## YEAR1998 -0.717
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0151852 (tol = 0.002, component 1)
Building The Best Interpretation Model
## Single term additions
##
## Model:
## DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
## Df AIC LRT Pr(>Chi)
## <none> 8437.8
## YEAR1998 1 8413.0 26.781 2.279e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Single term additions
##
## Model:
## DENSITY_INDEX ~ YEAR1998 + (1 | SPECIES_NAME)
## Df AIC LRT Pr(>Chi)
## <none> 8413.0
## DIET 7 8382.2 44.889 1.437e-07 ***
## SCIENTIFIC_FAMILY 11 8376.3 58.711 1.608e-08 ***
## LOCATION 10 8418.8 14.245 0.1621
## MARINE_RESERVE 1 8414.7 0.353 0.5525
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Single term additions
##
## Model:
## DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + (1 | SPECIES_NAME)
## Df AIC LRT Pr(>Chi)
## <none> 8369.7
## YEAR1998:DIET 7 8376.9 6.809 0.449
## YEAR1998:SCIENTIFIC_FAMILY 11 8345.4 46.336 2.82e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## df AIC
## M4_LMER 33 8476.756
## M5_LMER 35 8431.912
## df AIC
## M3_LMER 22 8426.150
## M6_LMER 24 8365.182
## df AIC
## M5_LMER 35 8431.912
## M6_LMER 24 8365.182
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8436.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6607 -0.6235 -0.0347 0.6186 3.8503
##
## Random effects:
## Groups Name Variance Std.Dev.
## SPECIES_NAME (Intercept) 0.1947 0.4413
## Residual 0.2653 0.5151
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.73686 0.03138 227.75030 55.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + (YEAR1998 | SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8357.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3173 -0.6166 -0.0355 0.6184 4.0456
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## SPECIES_NAME (Intercept) 0.280071 0.52922
## YEAR1998 0.001437 0.03791 -0.58
## Residual 0.253967 0.50395
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.854212 0.044437 166.901884 41.727 < 2e-16 ***
## YEAR1998 -0.015891 0.004004 114.793187 -3.969 0.000126 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## YEAR1998 -0.717
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0151852 (tol = 0.002, component 1)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + (YEAR1998 |
## SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8317.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3381 -0.6207 -0.0392 0.6299 4.0419
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## SPECIES_NAME (Intercept) 0.236515 0.48633
## YEAR1998 0.001482 0.03849 -0.67
## Residual 0.254096 0.50408
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.931554 0.242034 260.049362 7.981
## YEAR1998 -0.016475 0.004034 114.664449 -4.084
## DIETCoral -0.004182 0.200072 157.441219 -0.021
## DIETCrustaceans -0.149696 0.134728 177.301377 -1.111
## DIETEchinoids -0.483322 0.243909 215.696344 -1.982
## DIETFish -0.298709 0.143481 180.233550 -2.082
## DIETSponges -0.351583 0.144637 171.021021 -2.431
## DIETUnidentified -0.287404 0.134746 191.413786 -2.133
## DIETZooplankton 0.257555 0.152225 183.685227 1.692
## SCIENTIFIC_FAMILYCarangidae 0.267641 0.273837 255.497620 0.977
## SCIENTIFIC_FAMILYGobiidae 0.416543 0.236083 262.136891 1.764
## SCIENTIFIC_FAMILYHaemulidae 0.134310 0.247698 263.625905 0.542
## SCIENTIFIC_FAMILYHolocentridae 0.492765 0.273202 219.550493 1.804
## SCIENTIFIC_FAMILYLabridae 0.076967 0.243285 246.818026 0.316
## SCIENTIFIC_FAMILYLutjanidae 0.164076 0.262790 241.225835 0.624
## SCIENTIFIC_FAMILYOther 0.039461 0.217699 267.321114 0.181
## SCIENTIFIC_FAMILYPomacentridae 0.500062 0.247137 258.940678 2.023
## SCIENTIFIC_FAMILYScaridae 0.040181 0.263504 236.749545 0.152
## SCIENTIFIC_FAMILYSerranidae -0.075081 0.233853 254.686900 -0.321
## SCIENTIFIC_FAMILYSparidae 0.032139 0.294380 242.165587 0.109
## Pr(>|t|)
## (Intercept) 4.68e-14 ***
## YEAR1998 8.22e-05 ***
## DIETCoral 0.9833
## DIETCrustaceans 0.2680
## DIETEchinoids 0.0488 *
## DIETFish 0.0388 *
## DIETSponges 0.0161 *
## DIETUnidentified 0.0342 *
## DIETZooplankton 0.0924 .
## SCIENTIFIC_FAMILYCarangidae 0.3293
## SCIENTIFIC_FAMILYGobiidae 0.0788 .
## SCIENTIFIC_FAMILYHaemulidae 0.5881
## SCIENTIFIC_FAMILYHolocentridae 0.0727 .
## SCIENTIFIC_FAMILYLabridae 0.7520
## SCIENTIFIC_FAMILYLutjanidae 0.5330
## SCIENTIFIC_FAMILYOther 0.8563
## SCIENTIFIC_FAMILYPomacentridae 0.0441 *
## SCIENTIFIC_FAMILYScaridae 0.8789
## SCIENTIFIC_FAMILYSerranidae 0.7484
## SCIENTIFIC_FAMILYSparidae 0.9132
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0134851 (tol = 0.002, component 1)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + YEAR1998 *
## SCIENTIFIC_FAMILY + (YEAR1998 | SPECIES_NAME)
## Data: CAYMAN_NO_ZEROS
##
## REML criterion at convergence: 8361.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2876 -0.6155 -0.0400 0.6280 4.0287
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## SPECIES_NAME (Intercept) 0.223818 0.47309
## YEAR1998 0.001315 0.03627 -0.65
## Residual 0.254134 0.50412
## Number of obs: 5208, groups: SPECIES_NAME, 231
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 2.293987 0.407711 369.459496
## YEAR1998 -0.064930 0.044064 435.740900
## DIETCoral -0.001590 0.199777 157.720462
## DIETCrustaceans -0.141255 0.134558 177.720666
## DIETEchinoids -0.476373 0.243428 216.381090
## DIETFish -0.293884 0.143249 180.574365
## DIETSponges -0.349200 0.144431 171.310290
## DIETUnidentified -0.283090 0.134521 191.656597
## DIETZooplankton 0.253398 0.152083 184.158217
## SCIENTIFIC_FAMILYCarangidae -0.489583 0.472019 288.984552
## SCIENTIFIC_FAMILYGobiidae -0.303293 0.447512 307.309706
## SCIENTIFIC_FAMILYHaemulidae -0.516095 0.440967 281.747513
## SCIENTIFIC_FAMILYHolocentridae 0.181904 0.453341 251.610551
## SCIENTIFIC_FAMILYLabridae -0.278444 0.422658 298.472131
## SCIENTIFIC_FAMILYLutjanidae 0.160720 0.443705 279.833435
## SCIENTIFIC_FAMILYOther -0.349424 0.397607 327.079900
## SCIENTIFIC_FAMILYPomacentridae 0.114640 0.424717 307.098730
## SCIENTIFIC_FAMILYScaridae -0.136882 0.437132 300.714423
## SCIENTIFIC_FAMILYSerranidae -0.416355 0.414234 313.878389
## SCIENTIFIC_FAMILYSparidae -0.308927 0.523212 266.910655
## YEAR1998:SCIENTIFIC_FAMILYCarangidae 0.093685 0.049787 332.517614
## YEAR1998:SCIENTIFIC_FAMILYGobiidae 0.089642 0.049401 409.214271
## YEAR1998:SCIENTIFIC_FAMILYHaemulidae 0.080383 0.047505 343.909396
## YEAR1998:SCIENTIFIC_FAMILYHolocentridae 0.040972 0.047919 294.589613
## YEAR1998:SCIENTIFIC_FAMILYLabridae 0.046633 0.046417 358.841600
## YEAR1998:SCIENTIFIC_FAMILYLutjanidae 0.003729 0.047315 320.827602
## YEAR1998:SCIENTIFIC_FAMILYOther 0.051300 0.044484 419.878598
## YEAR1998:SCIENTIFIC_FAMILYPomacentridae 0.051539 0.045756 351.506074
## YEAR1998:SCIENTIFIC_FAMILYScaridae 0.026291 0.046149 342.381198
## YEAR1998:SCIENTIFIC_FAMILYSerranidae 0.045119 0.045528 390.951745
## YEAR1998:SCIENTIFIC_FAMILYSparidae 0.045181 0.054649 312.773273
## t value Pr(>|t|)
## (Intercept) 5.627 3.64e-08 ***
## YEAR1998 -1.474 0.1413
## DIETCoral -0.008 0.9937
## DIETCrustaceans -1.050 0.2953
## DIETEchinoids -1.957 0.0516 .
## DIETFish -2.052 0.0417 *
## DIETSponges -2.418 0.0167 *
## DIETUnidentified -2.104 0.0366 *
## DIETZooplankton 1.666 0.0974 .
## SCIENTIFIC_FAMILYCarangidae -1.037 0.3005
## SCIENTIFIC_FAMILYGobiidae -0.678 0.4985
## SCIENTIFIC_FAMILYHaemulidae -1.170 0.2428
## SCIENTIFIC_FAMILYHolocentridae 0.401 0.6886
## SCIENTIFIC_FAMILYLabridae -0.659 0.5105
## SCIENTIFIC_FAMILYLutjanidae 0.362 0.7175
## SCIENTIFIC_FAMILYOther -0.879 0.3801
## SCIENTIFIC_FAMILYPomacentridae 0.270 0.7874
## SCIENTIFIC_FAMILYScaridae -0.313 0.7544
## SCIENTIFIC_FAMILYSerranidae -1.005 0.3156
## SCIENTIFIC_FAMILYSparidae -0.590 0.5554
## YEAR1998:SCIENTIFIC_FAMILYCarangidae 1.882 0.0607 .
## YEAR1998:SCIENTIFIC_FAMILYGobiidae 1.815 0.0703 .
## YEAR1998:SCIENTIFIC_FAMILYHaemulidae 1.692 0.0915 .
## YEAR1998:SCIENTIFIC_FAMILYHolocentridae 0.855 0.3932
## YEAR1998:SCIENTIFIC_FAMILYLabridae 1.005 0.3157
## YEAR1998:SCIENTIFIC_FAMILYLutjanidae 0.079 0.9372
## YEAR1998:SCIENTIFIC_FAMILYOther 1.153 0.2495
## YEAR1998:SCIENTIFIC_FAMILYPomacentridae 1.126 0.2608
## YEAR1998:SCIENTIFIC_FAMILYScaridae 0.570 0.5693
## YEAR1998:SCIENTIFIC_FAMILYSerranidae 0.991 0.3223
## YEAR1998:SCIENTIFIC_FAMILYSparidae 0.827 0.4090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0168513 (tol = 0.002, component 1)


K Means Clustering
1998 K-MEANS
## K-means clustering with 4 clusters of sizes 3, 197, 45, 1
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 3.3708185 -5.838370
## 2 -0.4338479 0.121128
## 3 1.6524260 0.121128
## 4 0.9964154 -11.797868
##
## Clustering vector:
## [1] 2 2 2 2 3 2 2 2 3 2 2 2 3 3 3 2 2 2 2 2 2 2 1 2 2 2 2 3 3 2 2 3 2 2 2 2 3
## [38] 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 3 2 2 1 2 2 3 3 3 2 2 2
## [75] 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [112] 2 2 2 3 2 2 2 3 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 3 3 2 3 2 2 2 3 2
## [149] 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2
## [186] 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 3 3 2 3 2 2 3 2 3 2 2 2 3 2 2
## [223] 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 5.646235 17.475955 26.844551 0.000000
## (between_SS / total_SS = 89.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"

## [1] 3 197 45 1
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.413 0.701 4.98 0.168
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_98
## 1 3.3708185 -5.838370 2.7750663 4 3
## 2 -0.4338479 0.121128 0.1087986 5 197
## 3 1.6524260 0.121128 1.5708361 5 45
## 4 0.9964154 -11.797868 1.1111112 3 1
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.00 5 2
## 2 Arrow Blenny 0.00 5 2
## 3 Atlantic Spadefish 0.40 5 2
## 4 Balloonfish 0.60 5 2
## 5 Banded Butterflyfish 1.25 5 3
## 6 Bandtail Puffer 0.00 5 2
2000 K-Means
## K-means clustering with 4 clusters of sizes 1, 13, 21, 211
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 1.7907923 -15.62062947
## 2 3.2617558 0.06375767
## 3 1.6265220 0.06375767
## 4 -0.3713298 0.06375767
##
## Clustering vector:
## [1] 4 4 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 2 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 1
## [38] 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 2 4 4 4 4 4 4 4 4 4 2 3 4 2 4 4 2 3 4 4 4 3
## [75] 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [112] 3 4 4 3 4 4 3 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 2 4 4 3 4 4
## [149] 4 4 2 4 2 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 2 4 4 4 4 2 4 4 4 4 4 4 4 4 4
## [186] 4 4 4 4 3 4 4 4 4 3 4 4 3 3 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 2 4 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 3 4 4 4
##
## Within cluster sum of squares by cluster:
## [1] 0.000000 2.656586 5.140756 11.037111
## (between_SS / total_SS = 96.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 1 13 21 211
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.338 0.705 7.99 0.191
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_00
## 1 1.7907923 -15.62062947 1.60000006 5 1
## 2 3.2617558 0.06375767 2.63654775 8 13
## 3 1.6265220 0.06375767 1.48424325 8 21
## 4 -0.3713298 0.06375767 0.07641189 8 211
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.000 8 4
## 2 Arrow Blenny 0.375 8 4
## 3 Atlantic Spadefish 0.000 8 4
## 4 Balloonfish 0.375 8 4
## 5 Banded Butterflyfish 1.725 8 3
## 6 Bandtail Puffer 0.000 8 4
2002 K-Means
## K-means clustering with 4 clusters of sizes 28, 193, 1, 24
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 2.2038192 -2.3407942
## 2 -0.4705805 0.3360832
## 3 3.7637425 -7.7224331
## 4 1.0563062 0.3500253
##
## Clustering vector:
## [1] 2 2 2 2 4 2 1 2 2 2 2 2 1 1 4 2 2 2 2 2 2 2 4 2 2 2 2 1 1 2 2 2 2 2 2 2 3
## [38] 4 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1 4 1 2 2 2
## [75] 2 2 2 2 2 2 2 4 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 4 2 2 2 2 2 2 1 2
## [112] 2 2 2 4 2 2 1 4 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 4 2 2 4 2 4 2 1 2
## [149] 2 4 2 2 2 2 4 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2
## [186] 2 2 2 2 4 2 2 2 1 2 2 2 1 2 2 2 4 2 2 2 2 1 1 1 2 1 2 2 1 2 1 2 2 2 1 2 2
## [223] 2 2 2 2 2 2 4 2 2 2 2 2 2 2 4 4 2 2 2 2 4 2 2 1
##
## Within cluster sum of squares by cluster:
## [1] 10.408610 15.595991 0.000000 6.523836
## (between_SS / total_SS = 93.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 28 193 1 24
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.432 0.749 6.87 0.372
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_02
## 1 2.2038192 -2.3407942 2.08224209 6.000000 28
## 2 -0.4705805 0.3360832 0.08018755 6.994819 193
## 3 3.7637425 -7.7224331 3.25000003 4.000000 1
## 4 1.0563062 0.3500253 1.22321432 7.000000 24
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.0000000 7 2
## 2 Arrow Blenny 0.0000000 7 2
## 3 Atlantic Spadefish 0.0000000 7 2
## 4 Balloonfish 0.1428571 7 2
## 5 Banded Butterflyfish 1.4285714 7 4
## 6 Bandtail Puffer 0.1428571 7 2
2004 K-Means
## K-means clustering with 4 clusters of sizes 22, 202, 1, 21
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 1.0491517 0.06375767
## 2 -0.4151812 0.06375767
## 3 1.3180506 -15.62062947
## 4 2.8317720 0.06375767
##
## Clustering vector:
## [1] 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2
## [38] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 4 2 2 2 4 1 2 2 2 4 2 2 2 1 2 1 2 2
## [75] 1 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 4 2 2 2 2 2 2 2 4 4 2 2 2 2 2 4 4 1 2 4
## [112] 2 4 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 4 4 2 2 1 1 4
## [149] 2 2 2 2 4 2 4 2 2 2 2 2 2 2 2 2 2 2 1 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 4 4 2
## [186] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 4 2 2 2 1 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 2
##
## Within cluster sum of squares by cluster:
## [1] 4.715479 5.434402 0.000000 5.679612
## (between_SS / total_SS = 96.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 22 202 1 21
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.317 0.670 6.00 0.0638
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_04
## 1 1.0491517 0.06375767 1.00245042 7 22
## 2 -0.4151812 0.06375767 0.03916642 7 202
## 3 1.3180506 -15.62062947 1.17934056 6 1
## 4 2.8317720 0.06375767 2.17511388 7 21
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.0000000 6 2
## 2 Arrow Blenny 0.0000000 6 2
## 3 Atlantic Spadefish 0.0000000 6 2
## 4 Balloonfish 0.0000000 6 2
## 5 Banded Butterflyfish 0.3333333 6 2
## 6 Bandtail Puffer 0.0000000 6 2
2006 K-Means
## K-means clustering with 4 clusters of sizes 1, 201, 25, 19
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 1.4543713 -15.62062947
## 2 -0.4215216 0.06375767
## 3 1.1259748 0.06375767
## 4 2.9011636 0.06375767
##
## Clustering vector:
## [1] 2 2 2 2 2 2 2 4 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2
## [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 4 2 2 4 3 4 2 2 2 4 2 2 2 2
## [75] 3 2 2 2 2 2 2 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 2 2 2 2 2 4 4 3 3 4
## [112] 2 4 2 2 2 2 4 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 3 2 3 2 4 3 2 2 3 2 4
## [149] 2 2 2 2 4 3 4 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 4 2 2
## [186] 2 2 2 2 2 2 2 2 2 2 2 2 4 3 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 3 2 2 2 2 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 1 2
##
## Within cluster sum of squares by cluster:
## [1] 0.000000 5.995451 5.379587 4.182251
## (between_SS / total_SS = 96.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 1 201 25 19
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.324 0.661 8.00 0.0638
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_06
## 1 1.4543713 -15.62062947 1.28571423 7 1
## 2 -0.4215216 0.06375767 0.04560531 8 201
## 3 1.1259748 0.06375767 1.06861900 8 25
## 4 2.9011636 0.06375767 2.24215477 8 19
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.000 8 2
## 2 Arrow Blenny 0.000 8 2
## 3 Atlantic Spadefish 0.125 8 2
## 4 Balloonfish 0.000 8 2
## 5 Banded Butterflyfish 0.125 8 2
## 6 Bandtail Puffer 0.000 8 2
2008 K-Means
## K-means clustering with 4 clusters of sizes 1, 27, 195, 23
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 2.3529504 -15.62062947
## 2 0.9355029 0.06375767
## 3 -0.4532149 0.06375767
## 4 2.6419727 0.06375767
##
## Clustering vector:
## [1] 3 3 3 3 2 3 3 4 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 4 3 3 3 4 3 2 3 2 4 3 3 3 4 3 2 3 3
## [75] 3 3 3 3 3 3 3 4 3 3 2 2 2 3 3 3 2 4 3 3 3 3 3 3 3 2 4 3 3 3 3 3 4 4 2 3 4
## [112] 3 4 3 3 3 3 1 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 2 3 2 3 4 2 3 3 2 2 4
## [149] 3 3 2 3 4 2 4 3 3 2 3 3 3 3 3 2 3 3 2 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 4 2 3
## [186] 3 3 3 3 3 3 3 3 2 3 3 3 4 2 3 3 3 3 3 3 3 3 3 3 3 3 4 3 2 3 4 3 3 3 3 3 3
## [223] 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3
##
## Within cluster sum of squares by cluster:
## [1] 0.000000 3.924964 5.122044 6.192959
## (between_SS / total_SS = 96.9 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 1 27 195 23
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.373 0.725 8.00 0.0638
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_08
## 1 2.3529504 -15.62062947 2.08027203 7 1
## 2 0.9355029 0.06375767 1.05204472 8 27
## 3 -0.4532149 0.06375767 0.04465814 8 195
## 4 2.6419727 0.06375767 2.28993105 8 23
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.000000 8 3
## 2 Arrow Blenny 0.000000 8 3
## 3 Atlantic Spadefish 0.000000 8 3
## 4 Balloonfish 0.000000 8 3
## 5 Banded Butterflyfish 1.627083 8 2
## 6 Bandtail Puffer 0.000000 8 3
2010 K-Means
## K-means clustering with 4 clusters of sizes 160, 30, 5, 51
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 -0.6043733 0.136227
## 2 2.1358098 0.136227
## 3 1.4296039 -6.566141
## 4 0.4995571 0.136227
##
## Clustering vector:
## [1] 1 4 1 1 1 4 1 2 1 1 1 1 1 4 1 1 1 1 4 3 1 1 1 4 1 1 2 2 1 1 4 1 1 1 1 4 1
## [38] 1 1 4 1 1 1 1 1 1 1 1 1 1 4 4 4 2 1 1 2 1 1 1 2 2 4 4 4 2 1 1 1 4 2 4 1 3
## [75] 1 1 1 4 4 1 4 4 1 4 3 4 1 1 1 1 1 4 1 1 1 1 1 1 1 2 2 2 4 4 4 1 2 2 4 4 2
## [112] 1 2 1 4 2 1 4 1 1 1 1 1 1 4 1 1 2 1 1 1 1 1 1 1 1 1 4 1 4 1 2 4 1 1 2 4 2
## [149] 1 1 3 1 2 4 2 1 1 1 1 1 1 1 1 1 1 1 4 1 1 4 1 1 1 1 1 2 1 1 1 1 1 1 2 4 1
## [186] 1 2 1 1 4 1 1 1 4 1 1 1 2 2 4 1 1 1 1 1 1 1 4 1 1 1 2 1 1 1 2 1 1 1 4 1 1
## [223] 4 1 1 1 1 1 4 1 4 1 1 1 4 4 1 1 1 1 1 4 4 1 3 1
##
## Within cluster sum of squares by cluster:
## [1] 4.171866 7.603094 32.798465 7.143601
## (between_SS / total_SS = 89.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 160 30 5 51
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.522 0.749 7.98 0.179
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_10
## 1 -0.6043733 0.136227 0.0759519 8.997364 160
## 2 2.1358098 0.136227 2.1001345 8.997364 30
## 3 1.4296039 -6.566141 1.5784578 7.727063 5
## 4 0.4995571 0.136227 0.8914290 8.997364 51
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.0000 8 1
## 2 Arrow Blenny 0.5625 8 4
## 3 Atlantic Spadefish 0.0000 8 1
## 4 Balloonfish 0.0000 8 1
## 5 Banded Butterflyfish 0.1250 8 1
## 6 Bandtail Puffer 0.6250 8 4
2012 K-Means
## K-means clustering with 4 clusters of sizes 2, 40, 42, 162
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 0.8621329 -11.02288823
## 2 0.4481398 0.09035154
## 3 1.8956548 0.09035154
## 4 -0.6127615 0.09035154
##
## Clustering vector:
## [1] 4 4 4 4 2 4 2 3 2 4 4 4 4 2 4 4 4 3 3 2 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4
## [38] 4 4 2 4 4 4 4 4 4 4 4 4 4 2 4 3 2 4 4 3 4 4 4 3 4 3 3 2 3 4 4 4 3 4 4 4 1
## [75] 2 2 4 4 4 4 2 2 4 2 3 2 2 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 3 2 2 4 3 3 3 3 3
## [112] 2 3 4 4 4 4 3 4 4 4 4 4 4 2 4 4 3 4 4 4 4 4 2 2 4 4 2 4 2 4 3 2 4 4 3 2 3
## [149] 4 4 2 4 3 2 3 4 4 4 4 4 4 4 4 2 4 4 2 4 4 2 2 3 4 4 4 2 4 4 4 4 4 4 3 2 4
## [186] 4 4 4 4 4 4 4 4 2 4 4 4 3 3 4 4 4 2 4 4 4 4 3 3 4 2 3 4 4 4 3 2 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 2 4 4 3 4 4 1 3
##
## Within cluster sum of squares by cluster:
## [1] 4.734627 5.010843 11.221328 2.758980
## (between_SS / total_SS = 95.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 2 40 42 162
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.550 0.813 9.99 0.0900
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_12
## 1 0.8621329 -11.02288823 1.25092598 9 2
## 2 0.4481398 0.09035154 0.91433932 10 40
## 3 1.8956548 0.09035154 2.09120475 10 42
## 4 -0.6127615 0.09035154 0.05180039 10 162
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.0 10 4
## 2 Arrow Blenny 0.0 10 4
## 3 Atlantic Spadefish 0.0 10 4
## 4 Balloonfish 0.1 10 4
## 5 Banded Butterflyfish 0.6 10 2
## 6 Bandtail Puffer 0.2 10 4
2014 K-Means
## K-means clustering with 4 clusters of sizes 1, 169, 36, 40
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 -0.6386303 -14.61611025
## 2 -0.5562018 0.10256919
## 3 2.1321229 -0.13106064
## 4 0.4470079 0.05000248
##
## Clustering vector:
## [1] 2 2 2 2 3 2 3 2 2 2 2 2 3 3 4 2 2 4 2 2 2 2 3 2 2 2 2 3 3 2 2 3 2 2 2 2 3
## [38] 3 2 2 2 2 2 2 2 4 3 2 3 2 2 4 2 4 2 2 2 2 2 2 2 2 3 2 2 3 4 2 3 4 3 2 2 2
## [75] 2 2 2 4 2 2 3 4 2 4 2 2 2 2 2 4 2 2 4 2 2 2 2 2 4 2 2 2 2 2 4 2 3 2 2 4 4
## [112] 2 2 4 4 2 2 4 4 2 2 3 2 2 2 2 2 4 2 2 2 2 2 2 4 2 3 2 2 4 3 2 3 2 2 2 4 3
## [149] 2 2 2 2 2 2 3 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2 3 2 4 2 2 3 2 2 3 2 2 2 2 2 2
## [186] 1 2 3 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 3 2 2 4 3 3 2 4 2 2 4 2 3 2 2 2 4 2 2
## [223] 2 2 4 4 2 2 3 4 4 2 2 2 2 2 3 2 2 2 2 4 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 0.000000 3.921278 36.422495 9.192672
## (between_SS / total_SS = 89.9 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 1 169 36 40
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.507 0.794 9.95 0.476
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_14
## 1 -0.6386303 -14.61611025 6.968117e-09 3.000001 1
## 2 -0.5562018 0.10256919 6.548324e-02 10.000000 169
## 3 2.1321229 -0.13106064 2.201156e+00 9.888889 36
## 4 0.4470079 0.05000248 8.624584e-01 9.975000 40
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.000000 10 2
## 2 Arrow Blenny 0.000000 10 2
## 3 Atlantic Spadefish 0.000000 10 2
## 4 Balloonfish 0.450000 10 2
## 5 Banded Butterflyfish 2.119048 10 3
## 6 Bandtail Puffer 0.000000 10 2
2016 K-Means
## K-means clustering with 4 clusters of sizes 3, 10, 20, 213
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 2.6275241 -8.981689
## 2 3.7641263 0.110885
## 3 1.3479576 0.110885
## 4 -0.3402957 0.110885
##
## Clustering vector:
## [1] 4 4 4 3 2 4 4 4 4 4 4 4 3 2 4 4 4 4 4 4 4 4 2 4 4 4 4 1 2 4 4 4 4 4 4 4 4
## [38] 1 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 2 4 4 2 3 2 4 4 4
## [75] 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4
## [112] 4 4 4 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 3 4 4 4 4 4 4 3 4
## [149] 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4 4 1 4 4 4 4 4 4 4 4 4
## [186] 4 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 4 4 4 4 4 4 2 2 4 4 4 4 3 4 4 4 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4
##
## Within cluster sum of squares by cluster:
## [1] 6.775944 4.386883 5.016937 5.416670
## (between_SS / total_SS = 95.6 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 3 10 20 213
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.193 0.491 9.99 0.110
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_16
## 1 2.6275241 -8.981689 1.4839505 9 3
## 2 3.7641263 0.110885 2.0423332 10 10
## 3 1.3479576 0.110885 0.8553333 10 20
## 4 -0.3402957 0.110885 0.0259390 10 213
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.0000000 10 4
## 2 Arrow Blenny 0.0000000 10 4
## 3 Atlantic Spadefish 0.0000000 10 4
## 4 Balloonfish 0.8333333 10 3
## 5 Banded Butterflyfish 1.8500000 10 2
## 6 Bandtail Puffer 0.0000000 10 4
2018 K-Means
## K-means clustering with 4 clusters of sizes 53, 117, 72, 4
##
## Cluster means:
## MEAN_YEARLY_DI N_Sites
## 1 1.5649029 0.02820007
## 2 -0.8156263 0.12886692
## 3 0.1110118 0.12455030
## 4 1.1238945 -6.38491389
##
## Clustering vector:
## [1] 2 2 2 3 1 3 1 2 3 1 2 2 1 1 3 3 2 3 1 2 2 3 1 2 3 3 2 1 1 2 2 1 3 2 2 2 1
## [38] 4 2 2 3 2 2 2 3 1 1 2 1 3 2 3 2 3 2 2 2 2 2 1 1 3 1 1 2 1 2 2 1 1 1 2 2 2
## [75] 2 1 2 3 3 2 1 3 2 3 3 2 3 3 2 3 2 2 3 3 1 2 2 2 1 2 3 2 3 2 3 2 1 1 3 4 3
## [112] 2 3 3 1 3 2 1 3 3 3 1 3 2 3 2 2 3 2 2 2 2 2 2 3 2 1 2 3 1 3 3 3 3 2 2 1 1
## [149] 3 2 1 2 4 1 1 3 2 2 2 2 2 3 2 2 3 2 3 2 3 2 1 2 3 2 2 1 2 2 1 2 2 3 2 2 2
## [186] 2 2 2 3 1 2 3 2 1 2 2 2 1 2 2 2 3 2 3 2 2 3 1 1 3 1 3 2 1 2 1 3 2 2 3 2 3
## [223] 2 2 3 3 2 2 1 3 3 2 2 2 3 2 1 4 2 3 2 3 1 3 2 1
##
## Within cluster sum of squares by cluster:
## [1] 31.56526 16.01667 15.58508 47.09595
## (between_SS / total_SS = 77.5 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
## [1] 53 117 72 4
## [1] 53 117 72 4
## # A tibble: 1 x 4
## MEAN_DI SD_DI MEAN_SITES SD_SITES
## <dbl> <dbl> <dbl> <dbl>
## 1 0.833 0.838 9.91 0.495
## MEAN_YEARLY_DI N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_18
## 1 1.5649029 0.02820007 2.1440958 9.924528 53
## 2 -0.8156263 0.12886692 0.1493352 9.974359 117
## 3 0.1110118 0.12455030 0.9258102 9.972222 72
## 4 1.1238945 -6.38491389 1.7745536 6.750000 4
## SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1 Almaco Jack 0.300000 10 2
## 2 Arrow Blenny 0.100000 10 2
## 3 Atlantic Spadefish 0.400000 10 2
## 4 Balloonfish 1.500000 10 3
## 5 Banded Butterflyfish 2.103571 10 1
## 6 Bandtail Puffer 0.700000 10 3
Unscaled Cluster Centers
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 2.7750663 4 3.3708185 -5.838370
## 2 0.1087986 5 -0.4338479 0.121128
## 3 1.5708361 5 1.6524260 0.121128
## 4 1.1111112 3 0.9964154 -11.797868
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 1.60000006 5 1.7907923 -15.62062947
## 2 2.63654775 8 3.2617558 0.06375767
## 3 1.48424325 8 1.6265220 0.06375767
## 4 0.07641189 8 -0.3713298 0.06375767
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 2.08224209 6.000000 2.2038192 -2.3407942
## 2 0.08018755 6.994819 -0.4705805 0.3360832
## 3 3.25000003 4.000000 3.7637425 -7.7224331
## 4 1.22321432 7.000000 1.0563062 0.3500253
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 1.00245042 7 1.0491517 0.06375767
## 2 0.03916642 7 -0.4151812 0.06375767
## 3 1.17934056 6 1.3180506 -15.62062947
## 4 2.17511388 7 2.8317720 0.06375767
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 1.28571423 7 1.4543713 -15.62062947
## 2 0.04560531 8 -0.4215216 0.06375767
## 3 1.06861900 8 1.1259748 0.06375767
## 4 2.24215477 8 2.9011636 0.06375767
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 2.08027203 7 2.3529504 -15.62062947
## 2 1.05204472 8 0.9355029 0.06375767
## 3 0.04465814 8 -0.4532149 0.06375767
## 4 2.28993105 8 2.6419727 0.06375767
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 0.0759519 8.997364 -0.6043733 0.136227
## 2 2.1001345 8.997364 2.1358098 0.136227
## 3 1.5784578 7.727063 1.4296039 -6.566141
## 4 0.8914290 8.997364 0.4995571 0.136227
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 1.25092598 9 0.8621329 -11.02288823
## 2 0.91433932 10 0.4481398 0.09035154
## 3 2.09120475 10 1.8956548 0.09035154
## 4 0.05180039 10 -0.6127615 0.09035154
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 6.968117e-09 3.000001 -0.6386303 -14.61611025
## 2 6.548324e-02 10.000000 -0.5562018 0.10256919
## 3 2.201156e+00 9.888889 2.1321229 -0.13106064
## 4 8.624584e-01 9.975000 0.4470079 0.05000248
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 1.4839505 9 2.6275241 -8.981689
## 2 2.0423332 10 3.7641263 0.110885
## 3 0.8553333 10 1.3479576 0.110885
## 4 0.0259390 10 -0.3402957 0.110885
## DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI N_Sites
## 1 2.1440958 9.924528 1.5649029 0.02820007
## 2 0.1493352 9.974359 -0.8156263 0.12886692
## 3 0.9258102 9.972222 0.1110118 0.12455030
## 4 1.7745536 6.750000 1.1238945 -6.38491389
K-Means Density Index Cluster Centers From 1998 to 2008 for Grand Cayman
Data
|
|
1998 Centers
|
2000 Centers
|
2002 Centers
|
2004 Centers
|
2006 Centers
|
2008 Centers
|
|
1
|
2.7750663
|
2.6365477
|
3.2500000
|
2.1751139
|
2.2421548
|
2.2899310
|
|
3
|
1.5708361
|
1.6000001
|
2.0822421
|
1.1793406
|
1.2857142
|
2.0802720
|
|
4
|
1.1111112
|
1.4842433
|
1.2232143
|
1.0024504
|
1.0686190
|
1.0520447
|
|
2
|
0.1087986
|
0.0764119
|
0.0801875
|
0.0391664
|
0.0456053
|
0.0446581
|
K-Means Density Index Cluster Centers From 2010 to 2018 for Grand Cayman
Data
|
|
2010 Centers
|
2012 Centers
|
2014 Centers
|
2016 Centers
|
2018 Centers
|
|
2
|
2.1001345
|
2.0912047
|
2.2011562
|
2.0423332
|
2.1440958
|
|
3
|
1.5784578
|
1.2509260
|
0.8624584
|
1.4839505
|
1.7745536
|
|
4
|
0.8914290
|
0.9143393
|
0.0654832
|
0.8553333
|
0.9258102
|
|
1
|
0.0759519
|
0.0518004
|
0.0000000
|
0.0259390
|
0.1493352
|
Specific Species Investigations
Here I will be investigating the clusters overall in terms of their
centers, but also as they relate to specific species of interest in
other studies.
The “Lionfish” has been shown to negatively impact reef abundance, so
how has their density changed over time? The same has been shown of the
Mahogony Snapper (Lutjanidae), so how has their density changed over
time? (They greatly decrease grunt Haemulidae populations)
Low sighting frequencies of groupers (Serranidae), use “Yellowmouth
Grouper”, “Nassau Grouper”, and “Black Grouper”, and parrotfish
(Scaridae ), use “Stoplight Parrotfish”, “Redband Parrotfish”, and
“Rainbow Parrotfish”, reflective of higher harvest pressure
Finally, algael abundance has been steadily increasing over the past
30 years on Grand Cayman, and studies have shown algal levels decrease
at sites with high parrotfish density, but they actually increase in
sites with high surgeonfish density (both are major herbivores). So, how
have these fish changed in abundance over time with the increasing food
supply? Is one decreasing and the other increasing?
Surgeonfish checked using: “Ocean Surgeonfish”
## SPECIES_NAME Year cluster LF_Cluster_Center
## 1 Lionfish 1998 2 0.10879860
## 2 Lionfish 2008 3 0.04465814
## 3 Lionfish 2014 4 0.08624584
## 4 Lionfish 2018 3 0.92581020
## SPECIES_NAME Year cluster MS_Cluster_Center
## 1 Mahogany Snapper 1998 2 0.10879860
## 2 Mahogany Snapper 2008 4 2.28993105
## 3 Mahogany Snapper 2014 4 0.08624584
## 4 Mahogany Snapper 2018 3 0.92581020
## SPECIES_NAME Year cluster NG_Cluster_Center
## 1 Nassau Grouper 1998 3 1.57083610
## 2 Nassau Grouper 2008 3 0.04465814
## 3 Nassau Grouper 2014 4 0.08624584
## 4 Nassau Grouper 2018 3 0.92581020
## SPECIES_NAME Year cluster RP_Cluster_Center
## 1 Rainbow Parrotfish 1998 3 1.5708361
## 2 Rainbow Parrotfish 2008 2 1.0520447
## 3 Rainbow Parrotfish 2014 3 2.2011560
## 4 Rainbow Parrotfish 2018 3 0.9258102
## SPECIES_NAME Year cluster OS_Cluster_Center
## 1 Ocean Surgeonfish 1998 3 1.57083610
## 2 Ocean Surgeonfish 2008 3 0.04465814
## 3 Ocean Surgeonfish 2014 3 2.20115600
## 4 Ocean Surgeonfish 2018 1 2.14409580
KABLES FOR THESE SPECIES
Density Index K-Means Cluster Movements of the Lionfish
|
Species
|
Year
|
Cluster Classification
|
Cluster Center
|
|
Lionfish
|
1998
|
2
|
0.1087986
|
|
Lionfish
|
2008
|
3
|
0.0446581
|
|
Lionfish
|
2014
|
4
|
0.0862458
|
|
Lionfish
|
2018
|
3
|
0.9258102
|
Density Index K-Means Cluster Movements of the Mahogony Snapper
|
Species
|
Year
|
Cluster Classification
|
Cluster Center
|
|
Mahogany Snapper
|
1998
|
2
|
0.1087986
|
|
Mahogany Snapper
|
2008
|
4
|
2.2899310
|
|
Mahogany Snapper
|
2014
|
4
|
0.0862458
|
|
Mahogany Snapper
|
2018
|
3
|
0.9258102
|
Density Index K-Means Cluster Movements of the Nassau Grouper
|
Species
|
Year
|
Cluster Classification
|
Cluster Center
|
|
Nassau Grouper
|
1998
|
3
|
1.5708361
|
|
Nassau Grouper
|
2008
|
3
|
0.0446581
|
|
Nassau Grouper
|
2014
|
4
|
0.0862458
|
|
Nassau Grouper
|
2018
|
3
|
0.9258102
|
Density Index K-Means Cluster Movements of the Rainbow Parrotfish
|
Species
|
Year
|
Cluster Classification
|
Cluster Center
|
|
Rainbow Parrotfish
|
1998
|
3
|
1.5708361
|
|
Rainbow Parrotfish
|
2008
|
2
|
1.0520447
|
|
Rainbow Parrotfish
|
2014
|
3
|
2.2011560
|
|
Rainbow Parrotfish
|
2018
|
3
|
0.9258102
|
Density Index K-Means Cluster Movements of the Ocean Surgeonfish
|
Species
|
Year
|
Cluster Classification
|
Cluster Center
|
|
Ocean Surgeonfish
|
1998
|
3
|
1.5708361
|
|
Ocean Surgeonfish
|
2008
|
3
|
0.0446581
|
|
Ocean Surgeonfish
|
2014
|
3
|
2.2011560
|
|
Ocean Surgeonfish
|
2018
|
1
|
2.1440958
|